eRm (version 0.9-2)

LRSM: Estimation of linear rating scale models

Description

This function computes the parameter estimates of a linear rating scale model (LRSM) for polytomuous item responses by using CML estimation.

Usage

LRSM(X, W , mpoints = 1, groupvec = 1, se = TRUE, sum0 = TRUE, etaStart)

Arguments

X

Input data matrix or data frame; rows represent individuals (N in total), columns represent items. Missing values are inserted as NA.

W

Design matrix for the LRSM. If omitted, the function will compute W automatically.

mpoints

Number of measurement points.

groupvec

Vector of length N which determines the group membership of each subject, starting from 1

se

If TRUE, the standard errors are computed.

sum0

If TRUE, the parameters are normalized to sum-0 by specifying an appropriate W. If FALSE, the first parameter is restricted to 0.

etaStart

A vector of starting values for the eta parameters can be specified. If missing, the 0-vector is used.

Value

• Returns on object of class eRm containing:
• loglik
  Conditional log-likelihood.
• iter
  Number of iterations.
• etapar
  Estimated basic item parameters (item and category parameters).
• se.eta
  Standard errors of the estimated basic item parameters.
• betapar
  Estimated item (easiness) parameters.
• se.beta
  Standard errors of item parameters.
• hessian
  Hessian matrix if se = TRUE.
• W
  Design matrix.
• X
  Data matrix.
• X01
  Dichotomized data matrix.

Details

Through appropriate definition of W the LRSM can be viewed as a more parsimonous RSM, on the one hand, e.g. by imposing some cognitive base operations to solve the items. One the other hand, linear extensions of the Rasch model such as group comparisons and repeated measurement designs can be computed. If more than one measurement point is examined, the item responses for the 2nd, 3rd, etc. measurement point are added column-wise in X. If W is user-defined, it is nevertheless necessary to specify mpoints and groupvec. It is important that first the time contrasts and then the group contrasts have to be imposed. Available methods for LRSM-objects are print, coef, model.matrix, vcov,summary, logLik, person.parameters.

References

Fischer, G. H., and Molenaar, I. (1995). Rasch Models - Foundations, Recent Developements, and Applications. Springer. Mair, P., and Hatzinger, R. (2007). Extended Rasch modeling: The eRm package for the application of IRT models in R. Journal of Statistical Software, 20(9), 1-20. Mair, P., and Hatzinger, R. (2007). CML based estimation of extended Rasch models with the eRm package in R. Psychology Science, 49, 26-43.

See Also

LLTM,LPCM

Examples

#LRSM for two measurement points
#20 subjects, 2*3 items, W generated automatically, first parameter set to 0,
#no standard errors computed. 

data(lrsmdat)             
res <- LRSM(lrsmdat, mpoints = 2, groupvec = 1, sum0 = FALSE, se = FALSE)
print(res)